Neutrinoless double beta decay (0νββ) is one of the most sensitive probes for physics beyond the Standard Model, providing unique information on the nature of neutrinos. In this paper we review the status and outlook for bolometric 0νββ decay searches. We summarize recent advances in background suppression demonstrated using bolometers with simultaneous readout of heat and light signals. We simulate several configurations of a future CUORE-like bolometer array which would utilize these improvements and present the sensitivity reach of a hypothetical next-generation bolometric 0νββ experiment. We demonstrate that a bolometric experiment with the isotope mass of about 1 ton is capable of reaching the sensitivity to the effective Majorana neutrino mass (|mee|) of order 10–20 meV, thus completely exploring the so-called inverted neutrino mass hierarchy region. We highlight the main challenges and identify priorities for an R&D program addressing them.